Strong convergence theorems for two parameter Vilenkin-Fourier series

Abstract

As main result we prove that certain means of the partial sums of two-parameter Vilenkin-Fourier series are uniformly bounded operators from Hp to Lp (0 < p ≦ 1). The Hardy space Hp (0 < p ≦ 1) will be defined by means of a diagonal maximal function. As a consequence we obtain a so-called strong convergence theorem for the Vilenkin-Fourier partial sums. Some dual inequalities are also verified for BMO spaces.

title = "Strong convergence theorems for two parameter Vilenkin-Fourier series",

abstract = "As main result we prove that certain means of the partial sums of two-parameter Vilenkin-Fourier series are uniformly bounded operators from Hp to Lp (0 < p ≦ 1). The Hardy space Hp (0 < p ≦ 1) will be defined by means of a diagonal maximal function. As a consequence we obtain a so-called strong convergence theorem for the Vilenkin-Fourier partial sums. Some dual inequalities are also verified for BMO spaces.",

author = "P. Simon and F. Weisz",

year = "2000",

month = jan

doi = "10.1023/A:1006787316897",

language = "English",

volume = "86",

pages = "17--38",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",

publisher = "Springer Netherlands",

number = "1-2",

}

TY - JOUR

T1 - Strong convergence theorems for two parameter Vilenkin-Fourier series

AU - Simon, P.

AU - Weisz, F.

PY - 2000/1

Y1 - 2000/1

N2 - As main result we prove that certain means of the partial sums of two-parameter Vilenkin-Fourier series are uniformly bounded operators from Hp to Lp (0 < p ≦ 1). The Hardy space Hp (0 < p ≦ 1) will be defined by means of a diagonal maximal function. As a consequence we obtain a so-called strong convergence theorem for the Vilenkin-Fourier partial sums. Some dual inequalities are also verified for BMO spaces.

AB - As main result we prove that certain means of the partial sums of two-parameter Vilenkin-Fourier series are uniformly bounded operators from Hp to Lp (0 < p ≦ 1). The Hardy space Hp (0 < p ≦ 1) will be defined by means of a diagonal maximal function. As a consequence we obtain a so-called strong convergence theorem for the Vilenkin-Fourier partial sums. Some dual inequalities are also verified for BMO spaces.